2009/06/16 by Teresa Arias-Marco, Arias-Marco, Teresa
Mathematics · #53C20 #53C21 #53C25 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20 #msc:53C21 #msc:53C25 #msc:53C30
paper · pdf · doi:10.48550/arxiv.0906.2890
7 pages
arxiv created 2010/01/05 · arxiv updated 2010/01/07
This is the appendix of the paper [T. Arias-Marco, Constant Jacobi osculating rank of U(3)/(U(1) × U(1) × U(1)), Arch. Math. (Brno) 45 (2009), 241--254] where we obtain an interesting relation between the covariant derivatives of the Jacobi operator valid for all geodesic on the flag manifold M6=U(3)/(U(1) × U(1) × U(1)). As a consequence, an explicit expression of the Jacobi operator independent of the geodesic can be obtained on such a manifold. Moreover, we show the way to calculate the Jacobi vector fields on this manifold by a new formula valid on every g.o. space.